Question

If uncertainty in the measurement of position and momentum of an electron are equal, then uncertainty in the measurement of its velocity ??

• A. 8 $\times$ 10${}^{12}$ m s${}^{-1}$
• B. 6 $\times$ 10${}^{12}$ m s${}^{-1}$
• C. 4 $\times$ 10${}^{12}$ m s${}^{-1}$
• D. 2 $\times$ 10${}^{12}$ m s${}^{-1}$

Answer 1

Answer: (A)

8 $\times$ 10${}^{12}$ m s${}^{-1}$

$\Delta$x.$\Delta$p $\ge h/4\pi$
$\Rightarrow$ $\Delta$p $\ge$ $\sqrt{\frac{h}{4\pi }}$ [$\because$ $\Delta$x = $\Delta$p(given)]

$\Rightarrow$ v $\ge$ $\sqrt{\frac{h}{4\pi }}$ = 8 $\times$ 10${}^{12}$ ms${}^{-1}$ [$\because$$\Delta$p = m $\Delta$v]